Question

The number of particles are given by- n= -D(n2-n1)/(x2-x1) are crossing the unit area perpendicular to x-axis in unit time,n1 and n2 are the number of particles per unit volume for the values of x meant to be x1 and x2. how to calculate the dimensional formula of diffusion constant D?

Answer 1

Given, n = $-D\left(\frac{n_2-n_1}{x_2-x_1}\right)$
$$\begin{gathered} D=\frac{n(x_2-x_1)}{-(n_2-n_1)} \\ Dimensionsofn=number/area/time=L^{-2}{T}^{-1} \\ Dimensionsof{n}_1,n_2=number/volume=L^{-3} \\ Dimensionof{x}_2-x_1=diff.betweentwopositions=L \\ Therefore,D=\frac{\left(L^{-2}{T}^{-1}\right)\left(L\right)}{(L^{-3})}=\left[L^2{T}^{-1}\right] \end{gathered}$$